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This paper introduces an algebraic framework for reconstructing non-Hermitian Floquet systems from observable traces, replacing generic exponential fits with finite-dimensional reconstruction based on characteristic polynomials. By leveraging Cayley-Hamilton and Hankel methods, the approach isolates invariant spectral data while clarifying identifiability limits imposed by symmetries and restricted observable algebras. The methodology offers a rigorous mathematical foundation for analyzing driven quantum systems, such as transmon qutrits and SSH chains, where leakage and disorder affect visibility.
Algebraic Tomography of Non-Hermitian Floquet Systems from Observable Traces
arXiv:2605.24555v2 Announce Type: replace Abstract: We formulate a framework of Floquet algebraic tomography for finite-dimensional non-Hermitian monodromy matrices from observable trace sequences $\zeta_n^{(O)}={\rm Tr}(OM^n)$. Since these sequences are constrained by the characteristic polynomial of $M$, the inverse problem is a finite-dimensional algebraic reconstruction problem rather than a generic exponential fit. We organize the reconstruction through the observable resolvent, spectral determinant, and Dirichlet spectral data, separating the common spectral skeleton from observable-dependent dressing. Cayley--Hamilton and Hankel methods recover the similarity-invariant spectral data, while multi-observable and Liouville-space extensions connect the construction to realization theory and tomography reconstruction. We further clarify the limits of identifiability from restricted observable algebras: the data determine a visible representative, micromotion can enlarge the sampled visible operator space, and exact symmetries impose residual invisible sectors. Two examples, a driven transmon qutrit and a finite non-Hermitian Floquet SSH chain, demonstrate leakage-induced visibility expansion, observable-dependent phase response, EP-accessible branch geometry, and disorder/probe-dependent observable-dimension readouts.
Abstract:We formulate a framework of Floquet algebraic tomography for finite-dimensional non-Hermitian monodromy matrices from observable trace sequences $\zeta_n^{(O)}={\rm Tr}(OM^n)$. Since these sequences are constrained by the characteristic polynomial of $M$, the inverse problem is a finite-dimensional algebraic reconstruction problem rather than a generic exponential fit. We organize the reconstruction through the observable resolvent, spectral determinant, and Dirichlet spectral data, separating the common spectral skeleton from observable-dependent dressing. Cayley--Hamilton and Hankel methods recover the similarity-invariant spectral data, while multi-observable and Liouville-space extensions connect the construction to realization theory and tomography reconstruction. We further clarify the limits of identifiability from restricted observable algebras: the data determine a visible representative, micromotion can enlarge the sampled visible operator space, and exact symmetries impose residual invisible sectors. Two examples, a driven transmon qutrit and a finite non-Hermitian Floquet SSH chain, demonstrate leakage-induced visibility expansion, observable-dependent phase response, EP-accessible branch geometry, and disorder/probe-dependent observable-dimension readouts.
v2: 52 pages, 9 figures, 2 tables. references added, typo fixed
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)
arXiv:2605.24555 [quant-ph]
(or arXiv:2605.24555v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.24555 Focus to learn more arXiv-issued DOI via DataCite
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